A two phase flow in a conduit is a flow which includes both gas and liquid, or gas and solid, or liquid and solid. An example of a gas/liquid two phase flow is water and air flowing in a pipe; an example of a gas/solid two phase flow is coal particles and air flowing in a pipe. Ultrasonic methods for determining the presence of a two phase flow in a conduit are known. See, e.g., US statutory invention registration No. H608. Essentially, an ultrasonic pulse is sent transversely through a pipe and if the flow is single phase (i.e. all liquid), a return pulse is detected after a time lag as a return echo which is strong and reasonably sharp off the far wall of the pipe. If gas bubbles are entrained in the liquid, there are multiple small reflections and diffusion or attenuation of the main return echo off the far wall of the pipe. If a two phase flow with a defined gas/liquid interface is present in the pipe, the return echo is fairly strong but earlier in time than in the situation where there is only liquid flow since the return echo bounces off the gas/liquid interface instead of the far wall of the pipe. Finally, if the flow has a defined gas/liquid interface and also gas bubbles in the liquid, there are multiple small reflections due to the bubbles in the liquid and the return echo is both attenuated and earlier in time than would be the case with only liquid flow. Such measurement methods, however, which only detect the presence of a two-phase flow, do not completely define the two phase flow.
Quality is the mass fraction of the two-phase flow that is in the gaseous phase. Quality together with mass-flow determines the amount of energy (enthalply) that is convected by the flow and thus is a key variable used to define the status of the flow system. Accordingly, quality and/or mass flow measurements are needed to fully define the flow. One reason that mass flow rate and the quality measurements are needed is to adjust the rate of one phase of the flow in a system.
A typical liquid/gas two phase flow comprises a liquid film in contact with part or all of the conduit wall (depending on flow parameters and flow orientation with respect to gravity). The liquid is largely separate from a continuous or intermittent vapor flow. Since an identifiable liquid-vapor interface exists, it is possible to analyze the geometry, flow rate, and axial pressure drop behavior of the liquid and vapor flow separately, equating boundary conditions as appropriate. If the thickness of the liquid flow in the conduit can be determined, various flow models can be used to predict film thickness versus quality for a number of mass flow rates. See, for example, Wallis, G. B., One-dimensional Two-Phase Flow, McGraw-Hill, New York, N.Y., 1969, pages 51-54, and 315-374; Lockhart, R. W. and Martinelli, R. W, "Proposed Correlation of Data for Isothermal Two Phase, Two Components Flow in Pipes", Chemical Engineering Progress, Volume 45, No. 1, 1949, pages 39-48; and Deissler, R. G., "Heat Transfer and Fluid Friction for Fully Developed Turbulent Flow of Air and Super Critical Water with Variable Fluid Properties", Transactions, ASME volume 76, No. 1, 1954, page 73.
But the precursor step of detecting the thickness of the liquid flow using ultrasonic methods is troublesome. The presence of bubbles of gas in the liquid flow, the presence of large waves of liquid traveling in the conduit, small scale thickness changes in the liquid/vapor interface, and other similar "chaotic" conditions within the conduit severely affect the ability to determine film thickness using ultrasonic techniques. If one or more of these conditions are present within the conduit, a plot of the return echoes from an ultrasonic transducer is not a good indicator of film thickness. Moreover, a low flow rate with a high quality results in a highly chaotic flow as does a high flow rate with a low quality. Such chaotic flows render known film thickness measurement techniques unreliable.
Therefore, a trace of the return echoes from such a chaotic flow alone is seemingly not a good indicator of film thickness. Other techniques for measuring the thickness of the liquid film that is usually in contact with the wall of the conduit include sampling, thermal probes, film conductivity or capacitance measurements, and gamma densitometry. Although each of these techniques exhibits strengths and weaknesses, no technique offers the advantages of reflective-mode ultrasound. Ultrasound techniques are non-invasive, offer rapid response, excellent long term accuracy and sensitivity, and are applicable to all working fluids over a very broad range of temperatures. Moreover, even if non-ultrasonic thickness measurement techniques are used, the various flow models used to evaluate flow quality and mass flow rates are based on a number of assumptions which can lead to inaccuracies. On the other hand, quality and/or mass flow measurements cannot be accurately taken without measuring film thickness or a related parameter, void fraction. Flow meters, for example, do not indicate how much of the flow is liquid or gas and flow meters cannot be used in all situations.
A typical gas/solid two phase flow, such as coal particles entrained in an air flow, generally comprises a rope like structure of coal particles travelling in the pipe. There are no current techniques which accurately measure the amount of coal in the pipe. Trial and error methods commonly used in coal power plant operation, can result in poor efficiency and air pollution. In order to optimize combustion, the amount of coal and the amount of air delivered to the burner must be known.
Therefore, in addition to determining the presence of a two phase flow, considerable research has been performed on various means of actually measuring two-phase flows. These efforts have largely attempted to characterize an average value of some aspect of the flow, such as a pressure drop, void fraction, film thickness, velocity, or density. One problem with this approach is that knowledge of any single value is not sufficient to define a two-phase flow. Two-phase flows comprise two separate flows (of phase A and Phase B) that interact in extremely complex ways. If average values are used, at least two independent quantities must be measured to define the flow. In addition, a given pair of observations, such as a pressure drop and a velocity, often does not provide a sensitive indication of the flow rates of phase A and phase B for a broad range of conditions. Thus, different combinations of observations are often needed for different flow conditions.
There are applications that can be well served by suitably developed instruments based on currently known averaging techniques. However, there are many more applications for which combinations of currently available averaging measurements will not provide desirable results. For example, some applications demand a completely non-invasive flow measurement. Others may be geometrically constrained, so that only instruments of a given size or shape may be used. Other applications may require accurate flow measurement over an extremely broad range of flow conditions. Still others may be very cost-driven, so that the instrument must be very inexpensive. The current invention offers the advantage that any meaningful measurement technique, used rapidly and persistently, can be used to determine the flows of both phases. Since every application permits at least some meaningful flow observation to be made, the current invention ensures that a practical instrument can be developed.
The approach of the subject invention arises from simple, but profound observations about two-phase flows. First, they are deterministic, in that they satisfy the laws of physics. Thus, while their evolution is extremely complex, there is an underlying order to the flow behaviors. The behavior of a given wave, particle, or bubble, although complicated, is not truly random.
Second, since they are deterministic and behave in a complex fashion, they are likely to be chaotic. The word "likely" is used here because it has not yet been proven in generality that fluid turbulence satisfies the mathematical definition of chaos. It is not yet known what (if any) kinds of complex behaviors are possible that are neither chaotic nor random. It currently is not possible to make generalities about the behaviors of such a system. For want of a more conclusive answer from topologists, and since the view of two-phase flows as chaotic is consistent with the evidence so far available, the current invention assumed that the two-phase flows of interest are chaotic.
Two-phase flows are dissipative, i.e. given the opportunity, any work that is imposed on them is eventually lost to viscosity. Thus, given an arbitrary initial condition (e.g., means of mixing at the inlet to the flow conduit), a two-phase flow will settle into a pattern of behavior that is similar to that of other flows with the same flows of phase A and phase B but different initial conditions. Actually, it is difficult to prove this conclusively without generating many flow conditions with a variety of initial conditions and comparing their properties in detail. However, it is a basic tenet of the arts of fluid mechanics and two-phase flow that this is the case: if this were not the case, it would not be possible to generate models or correlations of two-phase flow behaviors. This is also consistent with the properties of dissipative chaotic systems.
If two-phase flows are dissipative and chaotic, then key statements can be made about their behaviors. Principal among these is the existence of a single underlying behavior, a "strange attractor", the shape of which changes as flow parameters change. The strange attractor is an extremely complicated path (in mathematical phase space) that defines all trajectories of the system with time. It is limited to a finite portion of phase space and is a single unending, open (i.e., never repeating) path in which points that are initially near one another diverge rapidly from one another with time (called sensitivity to initial conditions). The conclusions that can be drawn from the existence of a strange attractor are far-reaching. The principal conclusion for current purposes is that any observation of the system behavior, made over a period of time, is a mapping of the strange attractor. If the observation is made with constant time increment between measurements, it is a smooth mapping. Any smooth mapping of a strange attractor contains an amount of information about the system behavior that is comparable to any other smooth mapping with the same time increment and measurement sensitivity. Thus, any of a variety of measurement methods may be used with a two-phase flow with equal conviction that meaningful information is obtained.
This line of discussion is fairly well established in the art of chaos theory, but by itself is not sufficient to permit the measurement of two-phase flows. The reason for this is that the argument does not disclose how the evolution of the flow observations can be related to the flow conditions. In fact, various researchers have attempted to relate two-phase flow conditions to time-series measurement. The best known of these are Jones, O. C. and Zuber, N., "The Interrelation between void fraction fluctuations and flow patterns in two-phase flow" Int'l J. of Multiphase Flow, v2, page 273-306, 1975; Hubbard, M. G., and Dukler, A. E., "The Characterization of Flow regimes for Horizontal two-phase flow: 1. statistical analysis of wall pressure fluctuations", Proceedings of the 1966 Heat Transfer and Fluid Mechanics Institute, Saad, M. A. and Miller, J. A. eds., Standard University Press, pages 100-121, 1966. Jones and Zuber identified liquid-gas flow regimes from the probability density function of X-ray attenuation measurements. Hubbard and Dukler identified flow regimes from frequency spectra of pressure signals from liquid-gas two-phase flows. In neither of these cases was the flow rate of either or both phases determined.
The technical literature has many references describing efforts to examine or develop instruments of various kinds to measure or characterize two-phase flows. Overviews include Hsu, Y. Y., and Graham, R. W., Chapter 12: Instrumentation for Two-Phase Flow, in Transport Processes in Boiling and Two-Phase Systems, McGraw-Hill, 1976; and Mayinger, F., Chapter 16: Advanced Optical Instrumentation, in Two-Phase Flow and Heat Transfer in the Power and Process Industries, Bergles, A. E., et al, editors, Hemisphere Publishing Company, 1981. The bulk of these efforts have generated results of sufficiently limited application to have remained largely of research interest. True two-phase flowmeters, i.e., instruments that purport to define the flows of both phases A and B, are not widely available on the commercial market.
In industrial practice, the most widely used instruments for two-phase flows have been photon attenuation instruments. These instruments determine the attenuation of photons (typically microwaves or gamma rays) as they pass through the flow. The greater attenuation of one phase than the other (essentially from higher density) is used to characterize the portion of the flow channel cross section that is filled with each phase. Alternatively, this may be viewed as characterizing the average density of the flow. Depending upon the specific geometry of the instrument, it may be rendered more or less sensitive or the distribution of the phases across the flow channel, and thus may be used to identify the flow regime (e.g., bubbly, slug, stratified, annular, or mist flows). These instruments provide only a rough indication of the flow condition, because their sensitivity to the amount of each phase that is present is limited. In particular, gamma densitometers are highly sensitive to even trace quantities of lead in a flow, severely limiting their accuracy in many applications of interest (most notably in petroleum pipelines). Despite the limitations of these instruments in their originally intended embodiment, they could be used to advantage with the current invention to accurately determine the flows of phases A and B.
To generate useful information about the flow rates of phases A and B, an attenuation measurement must be combined with some indication of flow velocity. Such an indication may be obtained by making attenuation measurements at two closely spaced stations along the flow duct and cross-correlating the resulting signals. The time delay of the peak in the cross-correlation curve corresponds to an approximate time delay for flow propagation. Dividing the spacing of the instruments by this time delay provides a characteristic velocity. The average flow density and this velocity can be correlated to the flow rates of phases A and B. Correlation is needed to correct for the inevitable "slip" that occurs between phases (because they do not flow with identical velocity).
Even with suitable calibration, the accuracy of cross-correlated attenuation measurements is limited because of the poor sensitivity of the density measurement for many flow conditions. This limited accuracy is implied in U.S. Pat. No. 4,683,759 to Skarvaag et al, wherein, this basic idea is used to measure liquid-gas two-phase flows. However, the determination of liquid and gas flow rates is discussed for only one specific flow regime, called slug flow, in which the liquid and gas flows are largely intermittent, and the peak in the cross-correlation function quite sharp.
Other instrument systems have been devised to observe two-phase flows. In U.S. Invention registration H608 to Goolsby, an ultrasonic measurement technique is used to determine whether gas is present in a liquid flow. In this instrument, echo-mode ultrasound is used to determine the location of the second major reflection interface (the first being between the liquid and the tube wall). If the time-off-flight of the acoustic wave is less than that associated with a full tube (second reflection from the far wall), then a liquid-gas interface is present. Actually, this approach has been used to study two-phase flows quantitatively for quite a few years.
In U.S. Pat. No. 4,193,291 to Lynnworth, an ultrasonic method of determining flow density is described. This technique is based on the different attenuation rates of torsion waves in a body depending upon the density of the fluid in which the body is immersed. Various embodiments are described that render the instrument more or less sensitive to the distribution of the phases in the flow duct. This instrument is limited to liquid-liquid or liquid-gas two-phase flows. One unfortunate aspect of this instrument is its intrusiveness into the flow. The protrusion of the instrument into the flow raises the potential for damage to the instrument from debris carried by the flow, generates an undesirable pressure drop and flow disruption, and requires seals between the instrument and the flow duct which reduce the reliability of the flow system. Another unfortunate aspect of this instrument is that no single embodiment is described that determines the average density across the entire flow cross section. Thus, each embodiment is applicable to a limited range of flow regimes. Further, the issue of fluid wetting is not addressed: if the liquid wets the material of the sensor, the apparent density may be skewed strongly toward the liquid density. Even with these limitations, the mechanism of this measurement approach could be used with the current invention to provide an accurate determination of the flow rates of phases A and B.
The aforementioned patent states that the density measurement may be combined with acoustic velocimetry to determine the flow rates of both phases. In acoustic velocimetry, an acoustic wave is propagated by one transducer downstream through the flow and its time-of-flight to another transducer measured. A second wave is propagated upstream to determine the propagation time against the flow. Comparison of these propagation times determines both the effective speed of sound of the flow and its propagation velocity. If acoustic velocimetry works in two-phase flows at all, the measurements would be very sensitive to the flow regime. For example, in annular flow, a continuous liquid film is in contact with the flow duct wall. Any acoustic waves that enter the flow will effectively "short circuit" through the liquid (with its very high sonic velocity and relatively low attenuation) so that only the liquid velocity (skewed by the acoustic wave path) would be measured. By contrast, in stratified flow, a liquid flow on the bottom of the flow duct is effectively separated from a gas flow in the top of the duct. If acoustic waves traveling through the liquid can couple sufficiently with the gas flow, then a velocity that is an average of the liquid and gas velocities will be measured. This velocity would be quite different from (much higher than) that of an annular flow, even though annular flows often occur at much higher velocities. Thus, the calibration of the instrument output with different flow conditions would involve some very strong nonlinearities likely to result in poor accuracy.
U.S. Pat. No. 4,991,124 to Kline describes a different ultrasonic instrument for determining a fluid density. This technique is based on determining the velocity of sound and rate of attenuation of acoustic energy in the fluid. Because this technique relies on multiple reflections of the acoustic energy, which would be extremely difficult to detect in two-phase flows, it probably could not be applied to a two-phase flow.
AEA Technology, of the United Kingdom, has publicized a two-phase flowmeter for use in oil and gas fields [Anonymous, "Non-Intrusive Meter Measures Oil and Gas Flows", competitive Edge, Issue 4, pg. 3, Spring, 1994. This instrument uses a pulsed neutron beam which counts hydrogen, carbon, oxygen, and chlorine atoms passing the sensing point. Short bursts of radiation are used to activate oxygen atoms, which can be tracked as they move to define a flow velocity (a second measurement method). This instrument employs two averaging techniques to determine the flow rates of (potentially) several phases. However, it depends upon the phases being of distinct compositions to define their flow rates separately. If the two phases were of the same composition (a so-called single-component two-phase flow), then only a total flow measurement would be obtained. While this system may prove effective for its intended application in oil fields, its cost, complexity, and operational limitations will limit its use elsewhere.